Question

which term of the a.p. -9 , -8.25 , -7.5 ............ is its first positive term?

Answer 1

Answer:

14th term.

Step-by-step explanation:

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Answer 2

Given,

A.P. = -9, -8.25, -7.5, ---

To find,

The number of the first positive term of the A.P.

Solution,

The 14th term of the A.P. -9, -8.25, -7.5,--- will be the first positive term.

We can easily solve this problem by following the given steps.

According to the question,

A.P. = -9, -8.25, -7.5, ---

The first term (a1) of the A.P. is -9 and the second term (a2)

is -8.25.

So, the common difference (d) can be found by subtracting the first term from the second term.

d = a2-a1

d = -8.25 -(-9)

d = -8.25+9

d = 0.75

Now, the term should be positive that is greater than zero.

Using the formula to find the nth term,

an = a +(n-1)d

an >0

a + (n-1)d > 0

-9 + (n-1)0.75 > 0

-9 + 0.75n - 0.75 > 0

-9.75 + 0.75n > 0

0.75n > 9.75 ( Moving 9.75 from the left-hand side to the right-hand side will result in the change of the sign from minus to plus)

n > 9.75/0.75

n > 13

Hence, the 14th term is the first positive term for the given series.